function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta


%J = (1./m *    (-y'*log(sigmoid(X*theta)) - ( 1 - y' ) * log (1 - sigmoid( X * theta)))) + (lambda / (2 * m)) * (theta.^2)
%grad = 1./m * X' * (sigmoid(X * theta) - y);

theta0 = [0; theta(2:end)];

J = (1/m *  sum(-y'*log(sigmoid(X*theta)) - ( 1 - y' ) * log (1 - sigmoid( X * theta)))) + (lambda / (2 * m)) * sum(theta0.^2)

grad = (X' * (sigmoid(X * theta) - y) + lambda * theta0)/m;

	
% =============================================================

end
